This interdisciplinary project aims at utilizing the mechanical, structural and biochemical properties of myosin II and V motor proteins to develop new mathematical models for describing the molecular mechanics of these processive and non-processive motor proteins. New models will be formulated in terms of stochastic differential equations through the innovative application of known mathematical, physical and statistical techniques, and numerical simulation by high performance computing. Models for single-molecule and ensemble molecular interaction will be formulated and analyzed in detail, and new data analytical techniques will be explored. Experimental data obtained from the laser trap and in vitro motility assays will be used for model verification and validation. The ultimate goal of this project is to obtain an experimentally testable theoretical framework for a complete interpretation of newly available data for the interaction between myosin motor proteins and actin filaments at both mesoscopic and macroscopic levels. Intellectual Merit: There has been some long-standing debate about myosin step size and problems associated with laser trap experimental measurements. Because of these drawbacks, a mathematical modeling approach will be of vital importance, providing potentially the only way to fully understand and interpret data from numerous experimental protocols. It is expected that the models will also apply to other molecular motors (e.g. kinesin, dynein, RNA polymerase). In fact, signaling proteins, such as G-proteins, share a remarkable homology to the catalytic domain of myosin so a cross fertilization can be obtained. Broader Impact: It is anticipated that the project will not only be eminently suitable for training present and future graduate students, and postdoctoral researchers. Currently there are three graduate students all of whom are members of the underrepresented minorities who will benefit from participating in this project. A cross-disciplinary course that presents paradigms from condensed matter physics, biophysical chemistry and applied mathematics that can be effectively applied to molecular motor proteins studies will be designed and implemented. Also, results from the project will be useful to biotechnological researchers studying molecular motor proteins at the nanotechnological level.